A crank, attached to a rope and bucket inside a well, is completely unwound and the bucket is at the bottom of the well. The crank's handle is at its farthest point from the

ground, 1.5 m. The handle is 0.5 m away from the middle of the crank. One full turn

of the crank raises the bucket 0.4 m.

a) Write an equation that models the distance of the crank's handle to the ground in

terms of the bucket's distance from the bottom of the well.

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?